Four metal rods each of length L and cross sectional area A are joined at point M. Thermal conductivities of MA, MB and MD are equal and that of MC is thrice that of MA. The end points A, B, C and D are kept in large reservoirs. Heat folws into the junction from B at a rate of `P(Js^(-1))` and C from at a rate of 3P. Heat flows out of D at a rate of 5P.
(a) Find the relation between temperatures of points A, B and C.
(b) Find temperature of `D` if temperature of A and M and `T_(A)` and `T_(M)` respectively.

Answer

(a) `T_(A)=T_(B)=T_(C)` (b) `T_(D)=6T_(M)-5T_(A)`